金属管材曲线型凹模挤压力的基础流函数法求解

采用基础流函数法对不同型线任意曲线凹模管材挤压过程进行力学建模、解析分析与数值求解, 得到了一种管材挤压力的计算方法及相应表达式, 并在MATLAB软件平台上编写了挤压力数值计算程序;经与工厂实测结果对比, 该文方法计算得到的挤压力与实测结果吻合良好, 最大相对误差仅为-5.4%, 计算精度优于主应力法和功平衡法;而且, 由于该方法避免了完备流函数法中未知系数的迭代求解, 其计算效率大大提高;综合表明, 该文基于基础流函数法的挤压力求解方法的计算精度和计算效率都能够更好地满足工程计算需要。     

Chebyshev多项式在锚链分析中的应用

依据水流作用下锚链的数值分析模型，提出了应用Chebyshev多项式拟合建立锚链张力与锚链顶端位置函数关系的近似方法，该锚链函数多项式可方便地用于波浪与锚泊结构物相互作用的实时模拟中。计算中按静水和有流两种情况，应用二维和三维Chebyshev多项式，建立了锚链顶端水平和垂向拉力与锚链顶端水平、垂向位置，及水流速度的函数关系。锚链分析模型采用分段外推－校正方法计算，在无流、均质锚链情况下，计算结果与解析解完全吻合。     

基于功率流分析的结构声优化研究

功率流有限元法是分析复杂结构振动能量密度和强度的有效方法。在文中,结合边界元声学方程,将法向功率流定义为目标函数进行结构噪声问题研究。在数值分析中,用遗传算法对一加肋板结构进行了优化计算分析。计算结果验证了该方法的可行性和有效性。     

微分求积模拟二维流体中流函数约束的施加方法研究

采用微分求积法数值求解流函数-涡度方程来模拟二维流体时会遇到流函数的超约束问题,即虽然流函数方程为二阶偏微分方程,但在每个固体边界上都存在两个约束条件:一个Dirichlet条件和一个Neumann条件。以二维驱动方腔流动为例,对该问题进行深入分析,进而提出一种新的超约束处理方法,即在边界涡度的计算中考虑Neumann条件,而仅将Dirichlet条件施加于流函数方程。数值结果显示该方法可行,且计算效率较高。同时给出前人提出的单层法和双层法进行比较。试算表明单层法对于网格数的奇偶性很敏感,不适于处理该问题。与双层法对比后发现:该方法计算精度较高,且由于回避了超约束问题而更加方便于使用。     

两端简支输流管道共振可靠度分析

采用基于Galerkin的加权残数法分析输流管道,利用 阶Galerkin截断建立试函数,推导出消除残数方程,得到输流管道的前 阶固有频率,并分析流速对固有频率的影响。建立输流管道共振可靠度的功能函数,利用点估计法计算功能函数的前四阶矩,采用修正Edgeworth级数法求得输流管道的共振可靠度,并讨论了流速对管道共振可靠度的影响。研究结果对于输流管道的防共振设计和共振可靠性评估具有参考价值。     

求解线接触热弹流润滑问题的多目标最优化方法

本文给出了求解线接触热弹流润滑问题中线非线性方程组的多目标最优化方法，该法把求解润滑油膜压力函数和油膜厚度函数的微分方程转化成为求解一个双目标优化问题，求得了压力和膜厚的解析解，所得结果符合热弹流润滑的经典理论。     

有限水深势流计算的下潜源法及圆球绕流水底效应分析

本文采用下潜源思想改进的H-S方法,运用“平面镜像原理”对有限水深中的任意形状无升力体绕流问题进行了研究,并编制了相应的程序以圆球绕流为例进行了数值计算。文中首先概述了下潜源法的基本思想,给出了有限水深的格林函数表达式。然后介绍了数值计算要点和若干技巧,对计算结果进行了详细分析。最后总结了下潜源法的特点,并深讨了水底效应的作用。     

有压管道中的凸体绕流

在压管道中凸体绕流的势流一般解可采用解析函数在辅助平面上获得。根据顺直管道势流可获解析解这一事实，在每一离散小间距中假设固壁边界为直线，可获得近似解析解。然后采用变量替换，可获得物理平面上的近似解析解。对拱型，半拱型，平台和三角形凸体绕流进行了计算。计算结果与实验资料吻合良好。     

弹流油膜光学测试系统的特性分析

光干涉法是弹流润滑膜厚度测量的最有效的方法之一。传统的理论认为光弹流干涉主要是双光束干涉，即光干涉强度是油膜厚度的余弦函数，通常应用该余弦关系分析弹流干涉图象。然而，几个光弹流实验均表明干涉强度随油膜厚度的变化同科弦规律有明显的偏离。应用薄膜光学理论对光弹流测试系统进行了分析，干涉强度的计算结果和实验数据吻合一致，弹流光学系统的多光束干涉本质和金属膜的光吸收特性是干涉强度偏离余弦分布的原因。     

分析法计算挡板流导

本文给出了分析法计算挡板流导的方法。某些计算结果与蒙特卡罗法计算结果进行了比较，分析法计算结果也较为满意。     

A computational stream function method for two‐dimensional incompressible viscous flows

This work concerns the development of a numerical method based on the stream function formulation of the Navier–Stokes equations to simulate two‐dimensional—plane or axisymmetric—viscous flows. The main features of the proposed method are: the use of the high order finite‐difference compact method for the discretization of the stream function equation, the implicit pseudo‐transient Newton–Krylov‐multigrid matrix free method for the stationary stream function equation and the fourth order Runge–Kutta method for the integration of non‐stationary flows. Copyright © 2005 John Wiley & Sons, Ltd.     

The localized differential quadrature method for two-dimensional stream function formulation of Navier–Stokes equations

Localized differential quadrature (LDQ) method is employed to solve two-dimensional stream function formulation of incompressible Navier–Stokes equations. Being developed by introducing the localization concept to the general differential quadrature (GDQ) method, the employment of LDQ method becomes efficient and flexible, especially for the simulations of large scale computations. By introducing the Lagrange stream function to vorticity transport equation, the governing equation—the fourth-order partial differential equation (PDE)—is derived. To stably obtain the solutions of the fourth-order PDE, a fictitious point method is included to treat the boundary conditions. To examine the present scheme, two different types of classic benchmark fluid flow problems are proposed, including driven cavity flow problems and backward-facing step flow problems. The good agreement of solutions demonstrate the robustness and feasibility of the proposed scheme. Conclusively, the LDQ method is sufficient and appropriate enough to simulate the solutions of stream function formulation of Navier–Stokes equations with various Reynolds numbers.     

Boundary elements and optimization for linearized compressible flows around immersed airfoils

For two-dimensional inviscid compressible flows the stream function may be used as the field variable. Although the relevant equation is nonlinear, it can be linearized for flows around slender bodies, such as airfoils. In multiply connected flow domains the boundary stream function values are not known a priori. In the present paper, an optimization approach is adopted to find these unknown values, as well as the entire solution field. In the proposed method of solution, the adjoint variable method of optimization is used to find the sensitivity coefficients of the objective function, which is constructed by using the Kutta condition. The boundary element method is used to discretize the flow and adjoint equations at each iteration of the optimization procedure. Numerical solutions are provided for two example problems for flows in a channel with one and two airfoils.     

FINITE ELEMENT SOLUTION OF INCOMPRESSIBLE FLUID–STRUCTURE VIBRATION PROBLEMS

In this paper we solve an eigenvalue problem arising from the computation of the vibrations of a coupled system, incompressible fluid – elastic structure, in absence of external forces. We use displacement variables for both the solid and the fluid but the fluid displacements are written as curls of a stream function. Classical linear triangular finite elements are used for the solid displacements and for the stream function in the fluid. The kinematic transmission conditions at the fluid–solid interface are taken into account in a weak sense by means of a Lagrange multiplier. The method does not present spurious or circulation modes for non-zero frequencies. Numerical results are given for some test cases. © 1997 by John Wiley & Sons, Ltd.     

A numerical investigation of the effect of boundary motion on viscous channel flow

The steady, laminar, incompressible flow past a moving boundary in the entry region of a two-dimensional channel is considered in this study. The formation of a separated region during the upstream motion of a section of the lower boundary is of particular interest. The size of the separated region depends on the Reynolds number, and on the velocity and length of the moving boundary as well. A numerical solution is obtained from the continuity and the complete Navier-Stokes equations, subject to the appropriate boundary conditions. The describing equations are expressed in terms of the vorticity and the stream function. The alternating-direction implicit method is used to solve the vorticity equation while the successive over-relaxation method is used to solve, the stream function equation. The present numerical scheme is second-order-accurate since both the finite-difference equations and boundary conditions have second-order accuracy.     

Flow past an impulsively started circular cylinder at high Reynolds number

The unsteady viscous incompressible flow around a circular cylinder is studied numerically for high Reynolds number. The two dimensional Navier-Stokes equation in stream function-vorticity formulation is solved. A fractional step method is used to solve the stream function equation while the vorticity transport equation is solved using a third order upwinding scheme. The computed solutions by the finite difference method agree reasonably well with the available experimental and other computational results at a Reynolds number of 9500 and 4500. These comparisons are for the initial stages of flow evolution when the wake bubble is symmetric.     

A numerical method for solving the two-dimensional unsteady solidification problem with the motion of melt by using the boundary-fitted co-ordinate system

A numerical method for solving the two-dimensional unsteady solidification problem with the motion of melt is proposed. The boundary-fitted co-ordinate system is applied to a treatment for the moving solid-liquid interface in cylindrical co-ordinates with a symmetry axis. An alternating-direction-implicit (ADI) method is used to solve the transformed equations of motion and energy, which are expressed in terms of the vorticity and stream function. Several examples are displayed.     

Motion of a viscoplastic body between two coaxial cones

The stream function is obtained in the form of an expansion in powers of 1/r. It is shown that the nature of the velocity distribution is determined by the basic function of the stream function. The results obtained are compared with experimental data.